Physics Chapter on Vectors and Scalars

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What defines a scalar quantity?

It has both magnitude and direction.

It can be represented as a vector.

It always requires vector addition.

It has magnitude but no direction. (correct)

What is the result of multiplying a vector by a negative real number?

The magnitude increases and direction reverses.

The vector is unchanged.

The magnitude decreases and direction remains the same.

The magnitude decreases and direction reverses. (correct)

What does a position vector represent?

The shortest path taken by an object between two points.

The vector showing the object's position relative to a reference point. (correct)

The overall distance traveled by an object.

The vector indicating only the starting point of movement.

Which statement about displacement vectors is correct?

Displacement vectors are not dependent on the path taken. Signup and view all the answers

What characterizes the interaction of vectors under the triangle law of addition?

Vectors can be drawn sequentially to form a closed triangle. Signup and view all the answers

In a two-dimensional coordinate system, how is a vector typically represented?

As a line segment with direction and magnitude. Signup and view all the answers

What does the term 'uniform circular motion' imply regarding vectors?

The speed is constant, but the direction of the velocity vector changes continuously. Signup and view all the answers

What is the principle behind combining scalars for vector addition?

Scalars are combined through ordinary algebraic operations. Signup and view all the answers

If vector $oldsymbol{C}$ is the sum of vectors $oldsymbol{A}$ and $oldsymbol{B}$, what can be inferred about their directions?

The resultant may point in either direction depending on magnitudes. Signup and view all the answers

What is the result of subtracting vector B from vector A using the graphical method?

A + (-B) Signup and view all the answers

Which law of vector addition states that the order of vectors does not affect the resultant?

Commutative Law Signup and view all the answers

What is the correct expression for finding the resultant of two vectors A and B in component form?

R = (Ax + Bx)i + (Ay + By)j Signup and view all the answers

In the context of vector addition, which property allows you to distribute a scalar across the addition of vectors?

Distributive Property Signup and view all the answers

When resolving vector A at an angle θ with the x-axis, what is the formula for the x-component?

Ax = A cos θ Signup and view all the answers

What equation defines the magnitude of vector A in a 3-dimensional space?

|A| = √(Ax^2 + Ay^2 + Az^2) Signup and view all the answers

Which of the following statements is false regarding vector addition?

The sum of two vectors is independent of their directions. Signup and view all the answers

What is the geometric interpretation of the parallelogram law of vector addition?

The resultant is equal to the diagonal of the parallelogram formed by the two vectors. Signup and view all the answers

If vector A makes angles α, β, and γ with the x, y, and z axes, respectively, how do you find its components?

Ax = A cos α, Ay = A cos β, Az = A sin γ Signup and view all the answers

Which equation correctly expresses the relationship between velocity and acceleration in a two-dimensional motion with constant acceleration?

$ ext{v} = ext{v}_0 + ext{a}t$ Signup and view all the answers

How can the position of an object in motion with constant acceleration be represented mathematically?

$x = x_0 + v_0t + rac{1}{2}at^2$ Signup and view all the answers

What is the primary benefit of representing motion in a plane using vector components?

It simplifies calculations by allowing independent analysis of each direction. Signup and view all the answers

In the context of relative velocity in two dimensions, what scenario best illustrates this concept?

A boat moving upstream against the current while measuring its speed relative to the shore. Signup and view all the answers

Which of the following statements accurately reflects the concept of acceleration in a plane?

Acceleration can change both the speed and the direction of motion. Signup and view all the answers

Considering the motion represented by vectors in a plane, what can be concluded about the direction of the resultant vector?

It can vary significantly based on the magnitudes and directions of component vectors. Signup and view all the answers

What is the relationship between the angle of projection and the range of a projectile?

The range is maximized at an angle of 45 degrees. Signup and view all the answers

How does the maximum height of a projectile relate to its velocity of projection?

Maximum height is directly proportional to velocity squared. Signup and view all the answers

What happens to the time of flight if the angle of projection is increased beyond 90 degrees?

Time of flight is not defined. Signup and view all the answers

Which of the following statements is true regarding the projectile motion in absence of air resistance?

The horizontal velocity remains constant throughout the flight. Signup and view all the answers

Which equation correctly describes the time of flight for a projectile launched at an angle θ?

T = 2usinθ/g Signup and view all the answers

If two projectiles are launched with the same initial speed but at different angles, how does their range compare?

The projectile with the angle closest to 45 degrees will have a greater range. Signup and view all the answers

Which factor has no effect on the maximum range of a projectile launched on level ground?

Mass of the projectile Signup and view all the answers

How is the range of a projectile affected if the initial velocity is doubled, while keeping the angle constant?

The range is increased fourfold. Signup and view all the answers

What is the maximum height reached by a projectile with an initial speed u and angle θ?

H = u²sin²θ/2g Signup and view all the answers

What is the angular displacement if the radius vector turns through an angle of 2 radians in a uniform circular motion?

2 radians Signup and view all the answers

Which statement about centripetal force in uniform circular motion is correct?

It acts as a variable force that changes direction. Signup and view all the answers

What is the formula for average angular velocity?

ω = θ / t Signup and view all the answers

What is the work done by centripetal force in uniform circular motion?

Zero work is done Signup and view all the answers

If a particle is undergoing uniform circular motion, what can be inferred about its kinetic energy?

Kinetic energy remains constant. Signup and view all the answers

In the formula for centripetal force F = mv²/r, what does the term 'r' represent?

The radius of the circular path Signup and view all the answers

Which of the following equations relates linear velocity to angular velocity?

v = ωR Signup and view all the answers

What happens to the power developed by centripetal force in uniform circular motion?

It remains zero. Signup and view all the answers

Which of the following correctly describes angular velocity?

Change in angular displacement per unit time Signup and view all the answers

Which of the following statements correctly characterizes angular position?

It is the angle made by the radius vector with a reference line. Signup and view all the answers